UC-NRLF 


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LIBRARY 

OF  THK 

UNIVERSITY  OF  CALIFORNIA. 

O-IKT  OF" 


Deceived 
^Accessions  No. 


Class  No  .  . 


BY 


ROBERT   STEVENSON,  C.E..M.E. 

Meml'ter  of  the  American  Institute  of  Mining  Engineers;  California  Academy 
-  iences:  Technical  Society  of  the  Pacific  r-oast.  etc.,  etc. 


TRADE  SUPPLIED  BY 

THE   SAN   FRANCISCO   NEWS   COMPANY 
SAN  FRANCISCO,  CALIFORNIA 


A    XK\V    POTKXTIAL    PRINCIPLE 
IX    XATURK 


ELASTICITY  A  MODE  OF  MOTION 

BEING    A    POPULAR    DESCRIPTION    OF 

A  NEW  AND  IMPOETANT  DISCOVEEY 
IN  SCIENCE 


\ 


Si 


PRICE  5O   CKNTS 


A   XE\V    POTENTIAL   PRINCIPLE 
IN    NATURE 


ELASTICITY  A  MODE  OF  MOTION 

BEIXG   A    POPULAR   DESCRIPTION   OF 

A  NEW  AND  IMPORTANT  DISCOVERY 
IN  SCIENCE 


BY 


ROBERT   STEVENSON,  C.E..M.E. 

Member  of  the  American  Institute  of  Mining  Engineers;  California  Academy 
of  Sciences;  Technical  Society  of  the  Pacific  Coast,  etc.,  etc. 


SAX  FRAXCISCO 

INDUSTRIAL   PUBLISHING   COMPANY 
APRIL,  ivx-, 


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t,  1895, 
—  BY  — 

ROBERT  STEVENSON,   C.  E. 


CIRCULAR   LETTER. 


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The  discovery  which  I  am  about  to  describe 
was  first  impressed  on  my  attention  twenty-eight 
years  ago,  when  a  student  attending  Sir  William 
Thomson's  class  in  the  old  college  of  Glasgow 
University.  But  I  did  not  thoroughly  appreciate 
the  importance  of  the  matter  until  about  fifteen 
years  ago.  Since  then,  although  cognizant  of 
the  true  cause  of  gravitation,  I  have  not  been  in 
a  position  to  take  advantage  of  the  immense 
power,  and  wonderful  insight,  that  such  knowl- 
edge confers. 

My  business  as  a  mining  engineer  requiring  all 
my  time  and  attention,  and  not  being  a  recog- 
nized authority  in  natural  sciences,  my  desultory 
efforts  from  time  to  time  to  call  the  attention  of 
the  recognized  authorities  on  the  subject,  to  the 
facts  of  the  case,  have  met  with  no  success. 

I  am  now  preparing  to  publish  my  notes,  con- 
taining the  mathematical  proofs  and  experiments 
by  which  I  have  established  the  truth  (to  my 
own  satisfaction)  of  the  great  principle  in  Nature 
which  is  an  intermediate  and  universal  agent 
between  the  spiritual  agency  of  force,  and  the 


4  PREFACE. 

material  energy  which  produces  gravitation  and 
evolution. 

I  have  so  far  been  able  to  trace  this  intermedi- 
ary principle,  as  the  great  potential,  and  con- 
servative energy  in  the  material  universe.  Its 
elastic  resistance  to  the  radical  forces  of  disper- 
sion, being  as  necessary  to  the  stable  existence 
of  a  molecule  as  it  is  to  that  of  the  planetary  sys- 
tems of  the  whole  universe. 

ROBERT  STEVENSON,  C.  E. 

Academy  of  Sciences,  San  Francisco. 
April  10,  1895. 


CONTENTS. 


Page. 
Preface 3 

ESSAY:  ELASTICITY  OF  MOTION  THE  TRUE  AND 
PROXIMATE  CAUSE  OF  UNIVERSAL  GRAVI- 
TATION — 

Article  (1)  The  Greatest  Natural  Principle 7 

(2)  Its  Utility 7 

(3)  Gravitation,  Its  History  and  Theories 8 

(4)  Purpose  of  this  Essay 8 

(5)  Newton,  His  Great  Work 8 

^6)  Newton,  His  Mistakes 8 

<7)  Central  Force 9 

<8)  Newton's  Law    9 

<9)  Centripetal  Force  Unnecessary 9 

(10)  Free  Motion 9 

<11)  Its  Resultant 10 

(12)  Difference  Between  Free  and  Constrained 

Motion 10 

<13)  (14)  Forthcoming  Work 11 

(15)  The  New  Theory 11 

(16)  Geometrical  Description 11 

<17)  Kinetic  Energy  as  Taught 12 

(18)  Kinetic  Stability  a  Reciprocating  Force.  13 
{19)  Ratio    of   Kinetic    Stability    to    Kinetic 

Energy " 13 

(20)  Orbital  Motion   Elastic 13 

{21 )  Limit  of  Deflecting  Force 14 

<22)  Force  of  Restitution 14 

(23)  Stability  of  Solar  System 14 

(24)  Molecular  Resistance 15 

{25)  Elliptical  Motion 15 

(26)  Rectangular  Stress . . .  ; 16 

(27)  Kinetics  versus  Kinematics 16 

(28)  Laws  of  Tension . .  .16 


b  CONTENTS. 

Article  (29)  Law  of  Attraction 17 

(30)  Law  of  Inertia 17 

(31)  Kinematical  Results 18 

(32)  Law  of  Specific  Gravities 18 

(33)  Sunless  Systems 18 

(34)  Action  at  a  Distance 19 

(35)  Discovery  on  which   the  New  Theory  is 

Based    19 

(36)  Experimental  Proof, 20 

(37)  Lord  Kelvin's  Suggestion 20 

(38)  The  Law  of  Superimposed  Motions 21 

(39)  Illustration  of  the  Law 21 

(40)  Different  Case  21 

(41)  Free  Motion.     Equation  of  Curve 22 

(42)  Mathematical  Proof  of  New   Theory.  ...   22 

(43)  Elastic  Motion 23 

(44)  Laws  of  Stellar  Phenomena 23 

(45)  Light,  Its  Production  and  Transmission.  .  23 

(46)  Heat 23 

(47)  Electricity 23 

(48)  The  Cause  of  Sun  Heat 23 

(49)  How  Kinetic  Stability  Overcomes  Gravity  24 

(50)  Inductive  Capacities  and  Tidal  Motion ...   24 

(51)  The  Abbe  Moigno's  Prophecy 24 

THE  NEW  KINETIC  THEORY  OF  GRAVITATION  — 
Part  I.     A  Paper  Read  Before  the  Technical  Society 

of  the  Pacific  Coast 26 

Part  II.  Supplement  to  the  Above,  Containing  Reply 
to  Discussion,  and  a  Description  of  Two 
Experiments  submitted  to  the  Univer- 
sity of  California  and  the  Stanford  Uni- 
versity    47 


ELASTInTT)F  MOTION 


THE   TRUE   AND    PROXIMATE   CAUSE   OF 
UNIVERSAL    GRAVITATION. 

(1)  It  may  appear  to  be  egotistic  in  me  to  say 
that   the   principle  of  Kinetic  Stability,   or   that 
which  produces  it,  which  I  call  The  Persistence  of 
Energy,    is   the   greatest   natural   principle    that 
science  has  ever  discovered,  and  when  it  becomes 
thoroughly  known,  it  will   lead  to  a  harvest  of 
knowledge  and  power  for  mankind,  such  as  the 
world  has  never  before  experienced. 

(2)  It  will  in  fact  prove  the  heavenly  key  to 
a  realm  of  spiritual  truth,  whose  grandeur  con- 
sists  in   this,    that   it   will   enable    mankind    to 
understand  Nature  better,  and  to  utilize  her  more 
intelligently  for  the  benefit   of  the    human   race 
and  the  glory  of  the  Divine  Individuality,  who 
has  created  by  the  spirit  of  His   power   all  the 
phenomena  of  the  universe. 


8  ELASTICITY    OF    MOTION. 

(3)  It   would   be   out   of  place   in    this   short 
explanatory    paper   to   enter   into    the   historical 
portion  of  the  subject   of  gravitation;    nor   do  I 
propose    to   discuss   the    merits   of    the   various 
theories  which  have   been  advanced   during  the 
last  three  hundred  years. 

(4)  I  propose  therefore  to  devote  myself  to  the 
exclusive  task  of  explaining  the  theory  and  its 
application,    which    I    am    about   to   publish,  so 
that  those  naturalists  who  take  an  interest  in  the 
great  physical  principles  may  understand  before 
hand,  and  be  prepared  to  criticise  the  work  when 
it  appears. 

(5)  Before  entering  on  the  explanatory  portion 
of  the  subject,   allow  me  to  say  that  to  the  illus- 
trious   Newton   belongs   the   great  and  undying 
honor  of  having  rescued   the   theory  of  gravity 
from  the  grasp  of  metaphysics,  and  established  it 
on  the  firm  basis  of  physical  science,  where  for 
two  centuries   it   has   resisted   every    attempt  to 
displace  it. 

(6)  And   if  it   should   be  the  duty  of  science 
now  to  acknowledge  that  Newton  was  mistaken, 
both  in  his  hypothesis  and  his  theory,  still  the 


ELASTICITY   OF   MOTION.  9 

credit  of  having  discovered  and  demonstrated  the 
law  of  the  inverse  square  of  the  distance,  by 
means  of  which  astronomy  has  made  such  great 
progress,  will  ever  remain  as  a  halo  of  glory 
around  the  illustrious  author  of  the  "  Principia." 

(7)  According  to  the  accepted  laws  of  motion, 
curvilinear  motion  is  impossible  without  a   cen- 
tripetal force. 

(8)  Newton  started   on  that  supposition,  and 
with    Kepler's   laws   as   mathematical   data,    he 
demonstrated  the  great  law  of  universal  gravita- 
tion, on  which  all  theoretical  astronomy  is  based, 
and   from  the  application  of  which   many  great 
discoveries  have   been   made   in   the  times,  dis- 
tances, and  motions  of  the  planets  and  comets  of 
the  solar  system. 

(9)  But  if  it  can  be  shown  that  the  hypothesis 
of  a  centripetal  force  is  unnecessary,  then  I  think 
there  will  be  no  difficulty  in  establishing  the  fact 
that  orbital  motion  in  free  space  is  not  caused  by 
centripetal  force. 

(10)  In   our  every-day   experience   it   is  very 
seldom  that  we  observe  a  case  of  free  motion  in 


10  ELASTICITY   OF   MOTION. 

free  space.  The  nearest  approach  to  it  that  we 
meet  with  is  in  the  case  of  the  cricketer,  and 
baseball  player,  and  curious  to  say,  both  of  them 
can  throw  a  "curved  ball,"  a  ball  which  on 
leaving  the  hand  of  the  thrower  is  made  to 
describe  a  horizontal  curvilinear  path;  and  I  can 
prove  that  if  it  were  not  for  the  resistance  of  the 
air,  and  the  force  of  gravity,  it  would  be  possible 
to  make  a  ball  describe  a  complete  horizontal  cir- 
cuit round  an  imaginary  point  as  a  center  with- 
out any  tension  between  the  center  and  ball. 


(11)  By    this   hypothesis   the   ball   receives  a 
longitudinal  and  transverse  energy  in  the  same 
plane  impressed  upon  it,  which  causes  it  to  de- 
scribe a  curvilinear  path,  or  in  other  words,  the 
resultant  of  two   transverse   rectilinear   energies 
given  to  a  free  body  in  free  space  is  curvilinear 
motion. 

(12)  What  we  have  been  taught  of  the  princi- 
ples of  the  composition  and  resolution  of  forces; 
motions,    energies,    etc.,  in    Dynamical   Science, 
will  predispose  us   to   criticise   that  proposition, 
but  if  we  will  consider  for  a  moment  the  different 
conditions  between  a  free  body  in  free  space  and 
a  body  which  is  constrained  to  move  in  a  fixed 


ELASTICITY   OF   MOTION.  11 

•direction,   we  will  see   that  the  principle   which 
applies  to  the  one  may  not  apply  to  the  other. 


(13)  As  I  have  said,  this  paper  is  only  explan- 
atory of  the  principles  on  the  proof  of  which  the 
new  theory  of  gravitation  rests. 

(14)  To  prove  all  the  propositions  necessary  to 
-establish  these  principles   requires   a  good-sized 
volume,  which  I  hope  to  have  ready  for  publica- 
tion in  a  very  short  time,   as  the  manuscript  is 
nearly  completed  now. 

(15)  To  thoroughly   understand  the   theory, 
astronomers  must  be  prepared  to  look  at  the  sub- 
ject from  a  different  point  of  view  than  that  from 

which  they  have  been  taught  and  accustomed  to, 
as  the  theory  bears  a  similar  relation  to  the  New- 
tonian theory,  that  the  Copernican  bears  to  the 
Ptolemaic,  and  in  both  cases  it  is  simply  the  dif- 
ference between  an  apparent  action  and  a  real 
action. 

(16)  In  the  following  diagram  let  us  suppose 
the  mass  m  to  be  a  body  moving  in  the  straight 
line  A  B,  and  for  simplicity's  sake  let   us  con- 


12 


ELASTICITY    OF   MOTION. 


sider  it  as  a  dynamical  particle,  moving  with 
uniform  velocity  v  in  the  direction  of  B  w?th 
independent  motion  in  free  space. 

FIG.  1. 


J) 


Then    the   kinetic   energy   of  m  = 


m  v 
2 


(17)  When  m  reaches  the  point  C,  let  us  sup- 
pose that  a  transverse  impulse  superimposes  on 
m  an  additional  kinetic  energy  E&  in  the  direc- 
tion of  H  along  C  H.  Now  m  is  moving  with 
twice  the  kinetic  energy,  and  therefore  its  result- 
ant velocity  is  represented  in  direction  and 


ELASTICITY   OF   MOTION.  13 

magnitude  by  the  straight  line  C  D,  which  is  the 
diagonal  of  the  parallelogram  COD  H,  that  is 
what  is  taught  in  the  universities  at  present, 
and  that  is  one  point  where  my  discovery  proves 
that  such  teaching  is  wrong. 

(18)  I   find  by   experiment,    and   I   can   also 
prove  it  by  physical  geometry,  that  m  when  mov- 
ing  with    kinetic   energy    along    A  B  has   also 
kinetic  stability,  due  to  what  I  call  its  persistence 
of  energy,  and  that  the  kinetic  stability  acts  as  a 
latent    or    potential    energy,    which    acts    with 
reciprocating  effect  against  a  deflecting  force  or 
impulse  along  C  H,  and  consequently  the  result- 
ant, instead  of  being  along  the  diagonal  C  D,  is 
along  the  curvilinear  line  C  /,  and  we  can  show 
that  the  path  is  elliptical. 

(19)  We  also  prove  that  the  kinetic  stability 
=  E*  of  m  along  A  B  is  equal   to   the   kinetic 
energy,  and  that  E^  -j-  E*  =  E  =  total  energy, 
or   vis   viva,    and   that   E$   the   kinetic  stability 
is   inversely   proportionate   to   E^   the   potential 
energy. 

(20)  By  these  propositions  we  prove  that  the 
motion  of  a  free  body,  such  as  a  planet,  is  elastic, 


14  ELASTICITY   OF   MOTION. 

and  that  its  orbit  is  due  to  the  superimposed  mo- 
tions, hence,  although  it  appears  to  be  attracted 
to  a  focus,  it  really  contains  within  itself  a 
couple  and  a  direct  force,  which  constrains  it  to 
move  in  its  orbit  without  any  attractive  or 
repulsive  force,  or  any  elastic  medium  of  any 
kind  whatever.  It  is  in  itself  endowed  with 
elastic  motion. 

(21)  I  can    also  prove  that  no  force,  however 
great,  unless  it  be  infinite,   can  ever  permanently 
deflect   a  free  moving  body  from  the  line  of  its 
previous  motion. 

(22)  L,et  m  be  acted  on  at  C  with  an  impulse 
as  great  as  you  please,  which  is  not  infinite,  and 
there  is  always  a  component  tending  to  bring  it 
back  to  the  line  A  B,  and  such  a  component  is 
inversely  proportionate  to  the  radius  of  curvature 
at  any  point  in  the  body's  motion. 

(23)  Now   this   fact   explains   the  stability  of 
the  solar  system.     Supposing  the  sun  had  kinetic 
energy    due     to    its    inertia     and     longitudinal 
velocity,     then    by    some     means    a     transverse 
impulse  is  superimposed  at  a  radial  distance  from 
its  center  of  inertia,  acting  as  a  couple  with  the 


ELASTICITY   OF   MOTION.  15 

kinetic  stability,  producing  rotation  as  well  as 
linear  velocity,  then  I  can  prove  that  the  whole 
energy  due  to  rotation  would  be  absorbed  into 
the  sun's  mass  as  heat;  -and  if  it  was  great 
enough  the  mass  would  become  incandescent,, 
and  sufficient  material  might  be  dispersed  as' 
incandescent  vapor  to  produce  a  nebulous  atmos- 
phere, stretching  to  the  very  confines  of  the 
present  solar  system,  out  of  which,  as  Laplace 
has  shown,  the  whole  planetary  system  could  be 
evolved  by  refrigeration,  and  the  persistence  of 
energy  of  the  molecular  vortices  within  the 
nebula. 


(24)  In  such  a  system  as  this,  we  can  prove 
that  the  tendency  of  each  molecule  to  return  to 
its  original  line  of  motion  (its  persistence  of 
energy)  would  always  cause  its  apparent  centri- 
petal energy  to  more  than  balance  its  centrifugal 
energy.  Hence  the  Force  of  Restitution. 


(25)  Returning  again  to  the  diagram,  Fig.  1, 
let  us  suppose  the  mass  m^  m2  m3  to  be  a  body 
moving  in  the  orbit  C  D  E,  which  we  will  sup- 
pose to  be  a  semi-  ellipse,  whose  center  is  O,  and 
the  foci  G  and  6\,  and  C  E  the  major  axis  or 
diameter,  which  we  may  extend  both  ways  to  A 


HI7BKSIT7 


16  ELASTICITY   OF   MOTION. 

and  B,  then  suppose  ml  to  move  from  C  to  D 
with  a  uniform  and  independent  motion. 

(26)  Then  according  to   the  usual  interpreta- 
tion of  the  Newtonian  laws  of  motion,  for  •?nl  to 
describe  the  curve  C  m1  D  it  is  necessary  that  it 
should  be  acted  on  by  a  force  towards  H  in  the 
tangent  C  H,  and  another  and  independent  force 
in  the  direction  C  E,  and  that  the  force  along 
C  E  should   always   be   at   right    angles   to  the 
tangent  at  any  point  of  the  curve  C  ml  D,  so 
that  when  the  body  m  reaches  ml  the  direction 
of  the  composite  forces  would  be  along  the  tan- 
gent to  the  curve  at  ml,  and  the  radius  vector 
ml    G   if  the  orbit  was   elliptical,   and    O  mt  if 
circular. 

(27)  Now  as   a  purely    geometrical,    or  kine- 
matical  problem,    that  way    of  looking   at    it  is 
correct,  but  when  we  have  to  deal  with  a  body 
which    has    the    physical    property    of    kinetic 
energy,  due  to  its  independent  motion,  we  have 
to  adopt  other  methods  than  that  used  by  New- 
ton   in    the    "  Principia "  to   correctly  solve  the 
problem. 

(28)  If  we  suppose  O  m1  to  be  a  string  fixed 
at  O  as  a  pivot,  and  attached  to  mlt  or  if  we  sup- 


ELASTICITY   OF   MOTION.  17 

pose  the  string  G  m^  G^  fixed  at  the  foci  G  and 
Gl  passing  through  the  center  of  m^  then  we 
know  that  such  an  arrangement  will  produce  cir- 
cular or  elliptical  motion  if  ml  be  acted  on  by  an 
independent  tangential  force,  such  as  that  along 
C  H  or  ml  ff^  and  the  tension  on  the  string 
would  vary  constantly  with  the  variation  of 
curvature,  and  be  proportional  to  the  curvature. 

(29)  Now  instead  of  the  string,  the  Newtonian 
theory  requires  an  attractive  force  at  one  of  the 
foci,  say  G,  acting  as  a  tension  between  G  and 
mlt  which  varies  as  the  multiple  of  the  masses  at 
G  and  m1  divided  by  the  square  of  the  distance 
between  their  centers  of  gravity,  which  is: 

G  X  *», ^  _  m  X  ml 

~JT^*     ~^~ 

is  the  Newtonian  expression  for  the  universal 
law  of  gravitation.  A  very  simple  law  when  we 
know  the  true  value  of  each  respective  mass,  and 
a  law  which  must  always  be  correct  when  the 
inverse  square  of  the  distance  is  used  to  calculate 
the  value  of  the  mass. 

(30)  It  is   not  unscientific   to  suppose   that  a 
force  may  decrease  as  the  square  of  the  distance 
increases,  on  the  other  hand,  it  is  not  only  un- 
scientific, but  it  is  perfect  nonsense  to  say  that 


18  ELASTICITY   OF    MOTION. 

the  resultant  force  of  attraction  between  two 
masses  varies  as  the  multiple  of  the  masses, 
when  we  know  that  the  natural  laws  only  require 
addition  instead  of  multiplication. 

(31)  But,     as    I    say,     for    pure    kinematical 

t-      1        m  X  mi  .       , 
motions  such  a  law  ™ — is  absolutely  correct 

when  the  value  of  the  mass  is  found  by  the 
inverse  square  of  the  distance. 


(32)  Now  whilst  such  a  law  may  give  us  the 
true  relative  motions  of  the  planets  and  comets  of 
the  solar  system,  it  can  never  give  us  the  true 
specific  mass  or  gravity,  or  the  specific  energy  of 
each  body  separately,  hence  the  limit  to  the 
utility  of  the  Newtonian  law.  The  law  is  indeed 
a  kinematical  law,  whereas  the  new  law  will  be 
kinetic,  and  therefore  become  the  great  law  of 
energy,  not  only  in  the  inorganic  but  also  in  the 
organic  and  spiritual  worlds,  and  on  the  proper 
application  of  this  law  not  only  does  the  conser- 
vation of  natural  energy  depend,  but  the  truth 
and  value  of  eternal  life  becomes  demonstrable. 


(33)  In  the  case  of  the  solar  system,  with  the 
sun  at  G,  and  the  planet  at  m\m2m^  the  centri- 
petal force  looks  as  if  it  might  be  attractive,  but 


ELASTICITY   OF   MOTION.  19 

if  there  had  been  no  sun  in  the  focal  center  of  the 
solar  system,  and  only  empty  space,  as  we  will 
show  might  happen  in  Nature,  then  the  theory 
of  attraction  could  never  have  existed. 


(34)  The  supposed  action  at  a  distance  we  will 
prove  to  be  only  apparent,  just  as  Ptolemy's  sup- 
posed motion  of  the  stars  round  the  earth  was 
apparent  only.  It  is  therefore  quite  unnecessary 
that  there  should  be  a  "plenum  of  vortices,"  or 
an  "elastic  semi- material  medium,"  filling  inter- 
planetary space  to  produce  attraction  or  apparent 
tension. 


(35)  My  theory  is  based  on  the  discovery 
that  a  mass  m  moving  with  uniform  or  accel- 
erated velocity  in  the  line  A  B,  with  indepen- 
dent motion  in  empty  space,  may  have  another 
independent  motion  superimposed  on  it  at  C, 
such  that  its  resultant  path  (due  to  these  two 
motions  alone)  would  lie  along  the  semi-ellipse 
C  D  E;  or  in  other  words,  that  the  resultant  of 
two  transverse  independent  free  motions,  which 
have  kinetic  energy  in  free  space,  lies  along  a 
curve  instead  of  the  diagonal  of  the  parallelo- 
gram, of  which  the  adjacent  sides  represent  the 
composite  motions. 


20  ELASTICITY   OF   MOTION. 

(36)  The   experimental   proof  of  this   fact   is 
very  simple  and  convincing.     Take  a  magnetized 
steel  ball  two  inches  in  diameter,  project  it  from 
a  spring  catapult  with  a  velocity  of  50  feet  per 
second  along  a  perfectly  flat  and  smooth  table, 
20  feet  long  by  6  feet  wide,  dust  the  top  of  the 
table   with  a  white  powder,  and  cover   the  ball 
with  lamp  black,  then  at  a  distance  of  one  "foot 
from    where  the  ball  leaves  the  catapult   spring 
have  a  fixed   electro  magnet   so  arranged  as  to 
give  an  instantaneous  transverse  repulsion  to  the 
ball  equal  in  energy  to   what  the   ball    received 
from    the    catapult,    and   the    line    of    resultant 
motion    will   be   seen   to   be    elliptical.      If    the 
experiment  was  carried  out  in  a  vacuum,  and  the 
surface  of  the  table  and  ball  were  perfectly  true 
and  smooth,  the  path  would  be  perfectly  ellipti- 
cal. 

(37)  At  one  time  I  thought  the  proof  could  be 
better   established   by    using  a   vacuum  tube  in 
some    tall     tower,     such    as    the     Metropolitan 
Tower,  but  Lord  Kelvin,  to  whom  I  mentioned 
the    matter,  thought  it   would  not    answer,    and 
after   considering  the  matter  I  saw  that  he  was 
right,   because  the  tower  being  a   portion  of  the 
earth,   a  body  falling  within  the  tower  would  be 
moving    under    constraint,     and    the    resultant 


ELASTICITY   OF   MOTION.  21 

motion  in  that  case  would  lie  along  the  diagonal 
of  a  parallelogram. 


(38)  The  rule  is:  That  when  an  independent 
motion  is  transversely  superimposed  on  a  con- 
strained motion  the  resultant  lies  along  the 
diagonal  straight  line,  but  when  an  independent 
motion  is  superimposed  on  another  independent 
free  motion,  the  resultant  is  along  a  continuous 
curve. 


(39)  For  instance,  if  a  man  walks  across  a 
railway  carriage  whilst  it  is  moving  in  a  straight 
line,  the  resultant  due  to  the  composition  of  the 
two  motions  is  the  diagonal  straight  Hne,  accord- 
ing to  the  well-known  principles  of  dynamics. 


(40)  On  the  other  hand,  if  the  man  was  to 
jump  from  the  side  of  the  moving  carriage,  and 
was  not  acted  on  by  any  other  forces  than  those 
due  to  his  own  kinetic  energy  (the  one  parallel 
to  the  carriage,  and  the  other  transverse),  then 
he  would  describe  an  elliptical  curve,  and  return 
to  the  point  he  jumped  from,  if  the  motion  of  the 
carriage  was  uniform. 


22  ELASTICITY   OF   MOTION. 

(41)  The  difference  in  these  two  cases  depends 
on  the  different  degrees  of  freedom  of  motion. 
In  the  first  case,  whilst  walking  across  the  mov- 
ing carriage,  the  mass  of  the  body  had  momen- 
tum in  the  direction  of  motion  of  the  carriage, 
and  kinetic  energy  in  a  transverse  direction; 
whereas  in  the  second  case  the  body  had  not 
only  kinetic  energy  transverse,  but  also  kinetic 
energy  parallel  to  the  motion  of  the  carriage, 
and  if  the  mathematicians  will  compound  these 
two  co-ordinates  they  will  find  at  once  that  the 
resultant  must  be  along  a  curve  whose  equation 
may  be  expressed  thus: 


. 

when  x  and  y  are  the  co-ordinates  of  the  body, 
and  x\  and  ji  the  semi  amplitudes. 

(42)  When  we  consider  the  difference  between 
momentum  and  kinetic  energy  it  will  be  found 
that  the  mathematical  proof  of  the  theory  is  not 
very    difficult,     and    by    adopting   a    method   of 
physical  geometry   the  proof  becomes   not   only 
convincing,   but  absolutely  correct  and  incontro- 
vertible. 

(43)  We  prove  thus  by  means  of  a  number  of 
propositions  that  free  motion  in  free  space  is  elas- 


ELASTICITY   OF   MOTION.  23 

tic,  and  follows  absolutely  the  laws  of  elasticity. 

(44)  That   the   same   laws  which   govern  the 
Stellar    phenomena    control    and    produce    the 
atomic  motions,  and  regulate  their  affinities  so  as 
to  produce  molecular  cohesion. 

(45)  That    light,    as    the    earliest    and    least 
material    energy  in  the  universe,    is   due  to  the 
vibratory  action  of  the  spirit  of  power,  or  accord- 
ing to  science  it  is  due  to  the  elastic  vibration  of 
radiating  atoms,  or  lines  of  force  in  a  non- mater- 
ial field  of  force. 


(46)  That  heat   is   caused  by  inter-molecular 
vibration. 


(47)  And  electricity  is  produced  by  the  inter- 
ference of  waves  of  molecular  disruption. 


(48)  That  the  sun's  heat  is  due  to  incan- 
descence produced  by  the  inter-molecular  vibra- 
tions of  the  superimposed  kinetic  energies,  due  to 
the  sun's  straight  and  rotary  motions,  and  that 
fact  can  be  proven  by  the  new  law  with  the  help 
of  Joule's  equivalent. 


24  ELASTICITY   OF   MOTION. 

(49)  It  can  also  be  proven  by  this  theory  that 
the  continuous  horizontal  velocity  of  a  free  body 
in  a  vacuum  near  the  earth's  surface  at  1,036  feet 
per  second  will  prevent  that  mass  from  falling  to 
the 'earth;  or,  in  other  words,  that  the  kinetic 
stability  of  a  body  moving  with  independent 
kinetic  energy  transverse  to  the  force  of  gravity 
may  tend  to  overcome  gravity  to  such  an  extent 
that  the  body  may  move  in  a  circle  concentric  to 
that  of  the  earth's  circumference. 


(50)  These,  and  a  number  of  other  facts 
regarding  the  motions  of  the  solar  system, 
especially  the  specific  energy  inherent  in  the 
mass  of  each  planet,  and  their  respective  indue-' 
tive  capacities,  both  for  light,  heat  and  electri- 
city; also  an  explanation  of  the  cause  of  the 
tides  according  to  the  new  theory,  will  be 
given  more  fully  in  the  book  I  am  about  to  pub- 
lish on  the  subject. 


(51)  In  conclusion  I  feel  bound  to  support  the 
prophetic  saying  of  that  great  seer  the  Abbe 
Moigno,  who  in  the  Cosmos  of  1852  declares: 

"That  if  there  is  anything  certain  in  this 
"world  it  is  that  the  molecules  of  bodies  and 
"  bodies  themselves  are  not  really  self  attractive; 
"  it  is  that  attraction  is  not  an  intrinsic  but  only 


ELASTICITY   OF   MOTION.  25 

"a  developed  force;  it  is  that  notwithstanding 
"everything  occurs  as  though  bodies  mutually 
"attracted  each  other;  it  is  incontestably  true 
"that  bodies  do  not  attract.  Newton,  as  Euler, 
"  as  every  philosopher  worthy  of  the  name,  has 
"seen  in  Nature  but  two  things,  inertia  and 
4 '  motion,  originally  impressed  by  a  free  will,  the 
"the  first  and  infinite  mover.  And  it  is  with 
"these  two  great  facts  of  inertia  and  movement 
"  that  advancing  science  shall  ultimately  explain 
"  all  the  phenomena  of  the  physical  world." 


THE    NEW    KINETIC    THEORY    OF 
GRAVITATION. 

[A  paper  read  before  the  Technical  Society  of  the  Pacific  Coast.] 
PART  I. 

The  old  established  theory  of  centripetal  force 
is  that  given  by  Sir  Isaac  Newton  nearly  three 
centuries  ago,  in  the  memorable  words  of  the 
' '  Principia  " :  ' '  That  every  particle  of  matter  in 
the  universe  attracts  every  other  particle,"  and 
that  every  deviation  from  a  straight  line  in 
absolute  free  motion  is  due  to  that  fact  of  mutual 
attraction. 

That  is  the  force  which  bends  the  body's 
motion  and  keeps  it  revolving  in  an  orbit. 

Newton  himself  in  the  "Principia  "  compares  it 
to  the  string  of  a  sling  which  keeps  the  stone 
from  flying  away  from  the  centre. 

Whilst  experimenting  with  bodies  at  high 
velocities,  I  found  that  it  was  not  necessary  to 
have  a  solid  centre  of  attraction  to  produce  this 
centripetal  force.  I  found  that  bodies  in  motion 
are  apparantly  attracted  to  imaginary  points, 
lines  and  planes,  where  no  attractive  force  can 
possibly  exist;  and  during  the  last  fifteen  years 
have  given  this  fact  some  study  in  my  spare 


THEORY   OF   GRAVITATION.  27 

hours,  and  have  discovered  what  I  think  is  the 
true  cause  of  this  centripetal  force,  and  am  now 
prepared  to  put  it  forward  in  a  definite  form  for 
the  acceptance  of  science. 

I  am  fully  aware  that  deep  rooted  and  estab- 
lished ideas  are  difficult  to  remove  in  the  scien- 
tific, as  well  as  in  the  religious  world. 

We  all  know  how  long  it  took  the  scientific 
world  to  comprehend  the  idea  that  it  was  the 
weight  of  the  air  which  forced  the  water  to  rise 
in  a  vacuum,  the  "  Fuga  Vacui "  having  been 
the  accepted  cause  for  thousands  of  years. 

We  also  know  how  successfully  the  great 
mathematician  Ptolemy  held  the  scientific  world 
in  mental  bondage  by  his  beautiful  theory  of  the 
earth  as  the  centre,  round  which  the  whole 
heavens  revolved  every  twenty-four  hours. 

Now  I  find  that  the  illustrious  Newton  has 
fallen  into  a  similar  delusion,  by  means  of  the 
analogy  of  the*  sling  and  stone  he  failed  to 
comprehend  the  possibility  of  constrained  motion 
in  an  orbit  without  a  pull  towards  the  centre  or 
the  focus  of  the  orbit.  At  first  sight  it  would 
appear  to  an  observer  that  there  must  be  a  pull 
to  divert  a  moving  body  from  the  line  of  its 
motion,  indeed  the  first  and  second  laws  of 
motion  in  dynamics  clearly  show  that  there  must 
be  such  a  force.  And  Newton  was  quite  justified 


28  THEORY   OF   GRAVITATION. 

in  calling  it  a  centripetal  force.  I  accept  his- 
definition  of  a  centripetal  force,  and  I  accept  his 
law  of  the  inverse  square  of  the  distance,  as  a 
true  but  empirical  law  of  force,  but  I  disagree 
with  his  theory  that  this  centripetal  force  is  in  its- 
nature  or  action  "  attractive." 

This  false  theory  of  attraction  has  done  much 
to  obstruct  the  progress  of  physical  science;  to  it 
is  due  the  fact  that  mathematical  analysis  is 
almost  powerless  in  dealing  with  high  speed 
machines,  and  fluid  motion  at  high  velocities,  and 
that  all  the  formulae  in  the  molecular  constitution, 
of  bodies  and  chemical  physics,  as  well  as  the 
motions  of  the  heavenly  bodies,  are  nearly  all 
empirical.  The  new  theory,  which  I  call  the 
Theory  of  the  Persistence  of  Energy,  will  when 
properly  understood  open  up  to  mathematics  a 
right  of  way  by  which  all  these  branches  of 
science  will  be  fully  explored. 

As  this  paper  is  only  intended  to  be  pre- 
liminary, and  to  give  just  sufficient  information 
as  to  lead  to  the  discussion  of  the  subject,  I  will 
confine  myself  to  the  first  principles  of  the  sub- 
ject where  they  diverge  from  the  established 
theory  of  attraction,  and  leave  the  application  of 
the  theory  until  we  have  satisfied  ourselves  that 
the  theory  itself  is  correct. 

As  you  may  be  aware  I  have  already  delivered 


THEORY   OF   GRAVITATION.  29 

-a  lecture  at  the  Academy  of  Sciences,  on  the 
historical  portion  of  the  theory  of  gravitation, 
and  there  discussed  the  Newtonian  theory  of 
attraction;  quoting  Newton's  own  words  to  show 
that  he  never  believed  in  the  innate  and  inherent 
force  of  attraction  in  matter,  but  he  always 
Tioped  to  be  able  to  prove  that  attraction  was 
caused  by  the  motion  of  an  'aetherial  medium. 
All  the  great  natural  philosophers  since  his  day 
have  worked  at  that  problem,  either  to  prove 
that  apparent  attraction  was  due  to  the  vibrations 
of  an  aetherial  medium,  or  to  the  vortices  of 
radiant  atoms. 

Faraday  came  nearest  to  an  acceptable  proof 
when  he  discovered  that  magnetic  attraction  was 
due  to  the  inductive  action  of  a  field  of  force, 
which  surrounds  the  poles  of  the  magnet. 

Now,  you  see  the  question  of  the  attraction  of 
matter  is  by  no  means  a  settled  question,  al- 
though the  editor  of  our  only  scientific  paper, 
in  discussing  my  lecture  before  the  Academy  of 
Sciences,  thought  I  was  trying  to  destroy  a  law 
of  nature;  and  consequently  made  some  silly 
remarks  about  me,  which  in  the  daily  press 
would  have  been  very  amusing,  but  from  a  scien- 
tific journal  and  the  only  scientific  journal  of  the 
Pacific  Coast,  makes  one  wish  for  a  scientific 
journal  which  understands  science. 


or  TH« 


UHI78ESITY 


30  THEORY    OF    GRAVITATION. 

Now  I  defy  any  scientist  of  standing  to  contra- 
dict me  in  the  assertion  that  science  has  never 
definitely  adopted  action  at  a  distance  ( as 
attraction  is  called)  as  a  scientific  truth.  It  has 
been  accepted  as  a  scientific  dogma  awaiting  the 
true  solution  of  the  cause  of  attraction,  hence  it 
is  quite  legitimate  on  the  part  of  any  scientist  to- 
try  to  solve  the  problem,  and  he  who  can  dis- 
cover the  true  cause  of  gravity  has  no  need 
to  be  ashamed  of  his  discovery. 

It  is  only  a  few  months  ago  since  the  greatest 
of  all  the  great  natural  philosophers  of  this  age, 
Lord  Kelvin,  stated  to  an  admiring  audience  of 
scientists  in  London,  that  this  great  problem  had 
for  fifty  years  been  constantly  in  his  mind, 
sleeping  and  waking  it  was  always  there,  and 
yet  we  are  told  by  our  only  scientific  press  that 
any  professor  who  would  spend  his  time  in 
trying  to  discover  the  cause  of  gravity  had  most 
assuredly  mistaken  his  profession.  Well  gentle- 
men, I  hope  before  we  are  through  with  the 
discussion  of  this  subject  there  will  be  no  doubt 
in  your  minds  as  to  which  has  mistaken  his- 
profession,  the  editor  of  the  scientific  press,  or 
your  humble  servant. 

In  my  lecture  before  the  Academy,  I  gave  six 
illustrations  of  motion,  which  in  each  case 
showed  the  impossibility  of  mutual  attraction 


THEORY   OF   GRAVITATION.  31 

between  matter,  but  I  will  in  this  paper  confine 
myself  to  one  crucial  test  of  the  attraction  of  the 
earth  to  matter  on  or  near  its  surface;  a  test 
which  this  Society  can  make  at  very  little 
expense. 

We  all  know  that  the  law  of  the  attraction  of 
matter  is  that  the  force  of  attraction  varies 
directty  as  the  product  of  the  two  attracting 
masses,  and  inversely  as  the  square  of  the  dis- 
tance from  their  respective  centers  of  gravity,  and 
that  the  force  is  constant  and  produces  uniform 
acceleration  in  both  bodies  toward  each  other. 

Now  according  to  that  law  a  projectile  moving 
at  right  angles  to  the  direction  of  the  attractive 
force  will  be  constantly  accelerated  towards  the 
centre  of  the  earth,  and  in  consequence  will 
describe  a  parabola  in  its  motion. 

Whatever  its  horizontal  velocity  may  be  it  will 
always  fall  sixteen  feet  in  the  first  second,  conse- 
quently it  requires  a  velocity  of  nearly  25,000 
feet  per  second  to  describe  a  concentric  curve,  to 
the  earth's  surface.  But  I  find  that  if  I  make  a 
catapult  projectile  travel  fifty  feet  in  half  a 
second,  the  projectile  instead  of  falling  four  feet 
in  that  time,  as  it  should  do  if  it  was  subject  to 
the  force  of  attraction,  it  only  falls  a  very  little 
over  eighteen  inches.  Now  this  is  a  crucial  test 
of  attraction. 


32  THEORY   OF   GRAVITATION. 

If  there  is  such  a  thing  as  attraction  in  matter, 
no  horizontal  velocity  less  than  25,000  feet  per 
second  will  prevent  the  projectile  from  falling  to 
the  earth.  Now  according  to  my  discovery,  and 
the  law  of  kinetic  stability,  a  horizontal  velocity 
of  1,036  feet  per  second  kept  constant  will  enable 
any  weight  of  projectile  from  falling  to  the  earth, 
and  I  will  explain  to  you  how  kinetic  stability 
produces  that  effect. 

First  then  we  know  that  any  mass  m  with 
velocity  v  in  a  straight  line  uninfluenced  by 
any  other  motion,  having  perfect  freedom,  has 

— —  as  its  kinetic  energy.     It  must  have  had  that 
2 

amount  of  work  expended  on  it  to  give  it  the 
velocity  v,  and  it  is  capable  of  doing  that  amount 
of  work  before  it  is  brought  to  rest. 

If  instead  of  a  mass  whose  inertia  is  propor- 
tional to  m  we  have  a  weight  w  on  the  surface  of 
the  earth  whose  acquired  acceleration  in  one 
second  in  falling  towards  the  center  of  the  earth 
is  g  =  32.2.  Then  if  E^  =  kinetic  energy  — 

— —      That  we  all  know;  there  is  no  difference 

o 

in  our  opinion  on  that  point. 

But  I  have  discovered  that  the  mass  m  or 
weight  w  has  not  only  kinetic  energy  in  the  line 
of  its  motion  but  it  acquires  kinetic  stability 
transverse  to  the  line  of  its  motion,  and  that  its 


THEORY   OF   GRAVITATION.  33 

kinetic  stability  always  varies  in  the  same  ratio 
as  its  kinetic  energy  varies.  Now  that  fact  is 
not  known,  nor  yet  accepted,  in  the  science  of 
mechanics  or  dynamics,  and  on  this  fact  depends, 
as  I  will  show  you,  the  whole  theory  of  gravita- 
tion and  the  true  cause  of  what  has  been  hitherto 
considered  as  due  to  the  mutual  attraction  of 
matter.  I  am  sure  every  one  of  you  in  your 
experience  must  have  noticed  that  the  greater 
the  velocity  given  to  a  body  it  became  more  diffi- 
cult to  deflect  it,  and  if  sufficient  force  was  not 
exerted  it  would  tend  to  oscillate,  or  appear  to  be 
attracted  to  the  line  it  was  previously  moving  in. 
You  have  all  noticed  how  a  spinning  top  recesses 
when  it  is  displaced  a  little,  and  how  a  gyroscope 
vibrates  across  the  line  of  its  motion;  how  a 
bicycle  keeps  erect  in  motion,  and  requires  con- 
siderable force  to  make  it  oscillate,  but  which 
when  at  rest  has  to  be  supported  from  falling. 

Those  of  you  who  have  seen  the  water  issuing 
from  a  monitor  with  a  500-foot  head  would  see 
the  difference  in  stability  from  the  same  water 
under  a  50-foot  head.  On  this  principle  depends 
the  ejector  and  injector,  and  various  other  me- 
chanical inventions  whose  mathematical  theory, 
for  want  of  this  simple  law  of  kinetic  stability,  is 
as  intricate  as  the  trigonometrical  epicycles  of 
Ptolemy  when  he  proved  that  the  sun  went 


34  THKORY   OF    GRAVITATION. 

round  the  earth,  to  the  satisfaction  of  himself  and 
all  the  scientific  papers  of  the  world  for  1,400 
years;  and  when  Copernicus  thought  the  same 
thing  would  happen  if  the  earth  simply  turned 
on  its  axis,  he  was  thought  an  eccentric  old  fool 
to  try  and  alter  the  laws  of  Nature  which  God 
had  established  from  all  eternity. 

They  even  went  so  far  as  to  say  that  he  might 
as  well  try  to  prove  that  two  and  two  make  nine 
as  to  prove  that  the  earth  turned  on  its  axis.  It 
was  a  terrible  idea  to  the  multitude  to  think  that 
the  earth  turned  on  its  axis,  and  the  comical 
illustrations  of  that  period  are  as  amusing  almost 
as  what  appeared  the  other  day  in  the  San  Fran- 
cisco papers  about  Prof.  Stevenson,  who  did 
not  believe  that  one  piece  of  matter  attracted 
another.  Well  let  it  pass,  we  are  content  to  be 
like  Copernicus,  persecuted  for  the  sake  of 
scientific  truth,  knowing  full  well  that  the  laugh 
will  turn  some  day. 

Now  if  a  body  has  kinetic  stability  equal  to 
its  kinetic  energy,  it  will  vary  as  the  square  of  the 
velocity  of  the  body,  and  in  different  bodies  as 
their  masses,  and  that  is  the  new  law  of  kinetic 
stability  for  a  body  moving  in  a  straight  line. 

Now  we  will  consider  the  motion  of  a  body  in 
an  orbit,  which  is  a  circle.  If  a  body  moving  in 
a  straight  line  has  kinetic  stability  equal  to  its 


THEORY   OF   GRAVITATION.  35 

kinetic  energy,  then  so  long  as  the  body  moves  in 
that  line  its  kinetic  stability  is  latent,  and  on  this 
fact  we  can  explain  many  of  the  latent  energies 
amongst  molecules,  such  as  the  latent  heat  of 
steam,  and  by  a  true  understanding  of  this  fact 
we  can  find  out  how  to  convert  all  their  latent 
energies  into  kinetic  or  work-producing  energies, 
which  will  be  one  of  the  earliest  outcomes  of 
the  application  of  this  discovery  to  mechanical 
and  economical  inventions. 

Now  let  us  investigate  circular  motion,  where 
the  kinetic  stability  has  been  all  transformed  into 
potential  energy,  and  we  will  find  that  the 
kinetic  stability  is  now  active  as  Newton's  centri- 
petal force,  the  centripetal  force  is  there,  but  it 
resides  entirely  in  the  moving  body,  not  in  the 
center  to  which  it  tends,  as  we  will  prove  when 
we  have  circular  motion  without  any  mass  in  the 
center  to  attract  the  body,  and  we  believe  there 
are  planetary  systems  in  the  universe  which  have 
no  sun  in  the  center  of  the  orbits,  and  what  we 
call  twinkling  stars  are  sunless  systems  whose 
planets  are  themselves  suns  revolving  round  a 
sunless  centre,  the  possibility  of  which  we  will 
prove  to  you  later  on. 

We  know  that  the  centrifugal  tendency  of  a 
body  constrained  to  move  in  a  circle  is  expressed 

for   the   same   body    in   different   circles   as  — 


36  THEORY    OF    GRAVITATION. 

where  r  is  the  radius  of  the  circle,  and  v  the 
linear  velocity  in  the  orbit.  Now  if  we  simplify 
the  problem  by  taking  a  circle  of  radius  1  we 
have  the  centrifugal  force  proportional  to  m  v2, 
that  is,  the  stress  on  the  cord  fixed  at  the  centre 
to  retain  the  body  in  the  circumference  of  the 
circle;  now  the  actual  stress  due  to  the  body  is 

772-  1) 

one  half  of  that,  viz:  —  —because  the  other  half 

2i 

of  the  stress  is  re- action  on  the  fixture  at  the  cen- 
tre, which  we  can  prove  by  replacing  the  fixture 
by  another  string  of  equal  length  fastened  to 
another  body  of  equal  mass,  moving  with  equal 
velocity  in  the  same. circle.  The  stress  is  now  the 
same,  although  there  are  two  bodies  instead  of 
one,  but  the  centrifugal  force  for  both  is  m  v2, 

therefore  for  the  one  it  must  be  -  - -—    and   this  is 

another  fact  from  which  many  mechanical  inven- 
tions will  follow. 

Now  the  centrifugal  tendency  due  to  the  circu- 
lar motion  of  the  body  is  proportional  to— — 
and  if  the  radius  of  the  circle  is  unity  it  is  pro- 
portional to  — ^~  •  Now  the  kinetic  energy  of 

the  body  moving  in  the  circle  at  right  angles  to 
the  centripetal  force,  which  counteracts  the  cen- 
trifugal, is  also  ——'hence  the  centrifugal  force 


THEORY   OF   GRAVITATION.  37 

is  equal  to  the  kinetic  energy,  and  the  kinetic 
stability  is  equal  to  the  kinetic  energy,  therefore 
the  kinetic  stability  is  equal  to  the  centripetal 
force,  and  as  we  have  shown  that  a  body  in  free 
motion  has  only  got  kinetic  energy  and  kinetic 
stability,  therefore  kinetic  stability  must  be  the 
same  as  the  centripetal  force,  or  force  of  attraction. 

Now7  we  will  prove  that  circular  motion  does 
not  require  any  string  to  hold  the  body  in  the 
curve,  and  such  being  the  case  there  can  be  no 
attractive  force. 

It  is  almost  an  impossibility  to  make  a  practi- 
cal experiment  in  free  space  to  show  the  effects  of 
kinetic  stability,  because  of  the  great  velocity 
required  to  overcome  gravity,  so  that  before  a 
body  can  be  said  to  be  moving  with  perfect 
freedom  on  this  earth  it  must  have  an  indepen- 
dent velocity  of  at  least  1,036  feet  per  second. 

I  suggested  the  following  experiment  to  Lord 
Kelvin  last  summer:  To  get  Sir  Edwin  Wat- 
kin's  permission  to  use  the  1,200-foot  tower  now 
being  built  near  London,  have  an  iron  tube  about 
four  feet  diameter  in  the  centre  of  the  tower,  so 
that  it  could  be  exhausted  of  air,  have  partitions 
of  steel  paper  every  ten  feet,  let  them  be  in  an 
electric  circuit,  so  that  a  record  would  be  made 
of  the  instant  a  bolt  fell  through  each,  and  the 
distance  from  the  centre. 


38  THEORY    OF    GRAVITATION. 

Drop  a  soft  iron  bolt  from  the  top  of  the  tower; 
have  an  electro-magnet  placed  200  feet  from  the 
top  of  the  tower,  of  sufficient  capacity  to  deflect 
the  bolt  in  its  passage  about  one  half  inch;  now 
if  such  a  bolt  had  a  uniform  velocity,  and  be 
deflected  by  an  impulse  it  would  in  its  further 
passage  continue  to  oscillate  across  the  original 
line  of  its  motion,  due  to  its  kinetic  stability,  or 
the  persistence  of  energy.  Such  an  experiment 
would  prove  the  elasticity  of  motion,  and,  as 
Lord  Kelvin  says,  if  proven  would  be  the  fulfill- 
ment of  the  golden  dream  of  science. 

Now  this  law  of  kinetic  stability  shows  that 
motion  is  elastic,  because  if  it  requires  a  force 
greater  than  the  body's  kinetic  energy  to  perma- 
nently deflect  a  body,  then  if  the  force  applied  be 
less  than  the  kinetic  energy  the  difference 
between  that  and  the  kinetic  energy  is  a  force  of 
restitution,  which  is  the  same  as  the  force  of 
gravity,  and  follows  the  same  law,  being 
inversely  proportional  to  the  square  of  the  dis- 
tance between  the  centre  to  which  the  body  tends 
and  the  centre  of  the  body  itself,  and  it  is  that 
unearned  increment  of  the  body's  kinetic  stability, 
which  we  call  the  force  of  restitution,  or  in  the 
case  of  the  planets  the  force  of  gravity,  and  that 
force  varies  in  all  conic  curves  inversely  as  the 
square  of  the  radius  vector.  Of  course  in  the 


THEORY   OF   GRAVITATION.  39 

case  of  the  circle  under  uniform  velocity  there  is 
said  to  be  no  force,  or  rather  the  centripetal  force 
is  balanced  by  the  centrifugal  force,  but  in  an 
ellipse  where  the  radius  vector  joining  the  focus 
towards  which  the  force  of  restitution  tends  and 
the  body,  the  force  of  restitution  is  inversely  pro- 
portional to  the  square  of  the  radius  vector. 

I  have  gone  over  all  Newton's  propositions 
respecting  this  force  in  the  "  Principia,"  and  this 
force  of  attraction  in  every  case  is  the  same  as 
the  force  of  restitution,  and  his  calling  it  an 
attractive  force  is  simply  a  case  of  mistaken 
identity,  in  fact  a  delusion  similar  in  every  way 
to  the  Ptolemaic  delusion.  The  centripetal  force 
appears  as  if  it  was  an  attractive  force,  but  is  in 
reality  only  a  force  of  restitution. 

Energy  in  its  most  general  sense  is  purely  a 
mode  of  motion,  there  must  be  resistance  coupled 
with  velocity,  and  if  m  =  the  resistance,  then 
m  v1  =  E  =  energy,  or  vis  viva,  but  m  may  be 
taken  as  small  as  you  please,  so  long  as  it  is  not 
nothing,  and  v  may  be  taken  as  great  as  you 

please  so  long  as  it  is  not  infinite. 

m  v*  . 

Kinetic  energy _=  E±  =  ~^  is  the  kinetic  en- 
ergy due  to  direct  force,  and  is  a  measure  of  the 
work  done  on  a  body  in  motion. 

Potential  energy  =  =  EP  =  the  capacity  of  a 
body  to  do  work. 


40  THKORY  OF  GRAVITATION. 

Kinetic  stability  =  Es  =  —^~  is  the  resistance 

offered  by  a  body  moving  with  independent  mo- 
tion to  change  of  direction,  and  is  always  recipro- 
cally proportional  to  the  potential  energy. 

Kinetic  stability  is  a  kind  of  latent  energy. 

Force  =f=  m  a,  is  the  imaginary  agent  by 
which  power  communicates  an  action  against  a 
resistance,  and  it  may  truly  be  called  the  spirit  of 
power.  An  effective  force  is  an  unbalanced  effort. 

We  divide  forces  into  two  general  classes  and 
several  specific  varieties. 

First. — Conservative  Forces  are  those  which 
increase  both  the  kinetic  stability  and  kinetic 
energy  at  the  same  time,  and  in  the.  same  pro- 
portion. 

Second. — Radical  Forces  are  those  which  in- 
crease the  potential  energy  at  the  expense  of 
the  kinetic  stability. 

Specific  kinds.  First  class  centripetal  force  = 
/cp  is  generally  the  tendency  of  a  body  in  motion 
to  return  to  the  original  line  of  its  motion  if  dis- 
turbed by  a  force  less  than  the  kinetic  stability  of 
the  body. 

Second  class  centrifugal  force  =  fc?  is  the 
tendency  of  a  body  to  move  from  the  centre, 
being  a  component  to  the  tangential  motion  of  a 
body  moving  in  an  orbit. 


THEORY   OF   GRAVITATION.  41 

Force  of  Restitution  /r  is  the  excess  of  the  con- 
servative forces  over  the  radical  forces,  and  it  is 
equal  to  the  unearned  increment  of  the  kinetic  sta- 
bility, and  is  the  same  as  Newton's  force  of 
attraction. 

PROPOSITION    I. 

Every  body  which  has  independent  motion  has 
kinetic  energy  equal  to  the  work  done  by  a  con- 
servative force  in  the  direction  of  its  motion  = 


m  =  the  specific  resistance  of  the  body  to 
change  of  motion,  and  v  the  velocity  generated 
by  the  action  of  a  conservative  force  in  time  t. 
Then  the  action  of  a  uniform  force  starting  from 

no  velocity  to  v  velocity  is  equal  to  - 

2i 

Now  R  s  =  work  done,  where  R  is  uniform 
resistance  and  s  =  distance.     Now  R  s  =fv  t  = 
m  z;2,  and  the  mean  work  when  /starts  from  O  is 
m  v1, 
~2~ 

PROPOSITION  II. 

Every  body  which  has  kinetic  energy  has  also 
kinetic  stability,  and  its  kinetic  stability  increases 
with  its  kinetic  energy. 

Let  a  body  moving  with  kinetic  energy  —  — 


42 


THEORY   OF   GRAVITATION. 


be  disturbed  transversely  in  its  course,  and  we 
know  that  the  force  necessar}7  is  directly  propor- 
tional to  the  square  of  the  velocity,  and  inversely 
as  the  radius,  now  if  the  mass  m  and  the  radius 
r  be  constant  the  force  varies  as  the  square  of  the 
velocity. 

Now  we  know  that  the  kinetic  energy  varies  as 
the  square  of  the  velocity,  hence  the  kinetic  sta- 
bility increases  in  the  same  ratio  as  the  kinetic 


energy,  from  m  to 


m  v 
2 


•it  i 


THEORY   OF   GRAVITATION.  43 

PROPOSITION    III. 

The  kinetic  stability  is  equal  to  the  kinetic 
-energy. 

Let  us  take  the  body  m  moving  with  velocity  v 
in  the  straight  line  A  B.  Hang  another  body 
mi  =  to  m  from  a  point  O  by  an  inextensible 
cord,  so  that  the  body  m\  will  be  at  rest  in  the 
straight  line  A  B,  and  m  will  impinge  and  give 
up  all  its  energy  to  ml.  See  Fig.  2. 

Now  mi  by  means  of  the  cord  and  fixture  at  o 
will  be  constrained  to  move  in  the  circumference 
of  a  circle  of  which  the  cord  is  the  radius,  and 
with  the  same  velocity  in  the  curve  that  it  had  in 
the  straight  line,  which  proves  that  it  has  the 
same  kinetic  energy  as  formerly. 

But  we  also  become  cognizant  of  another  stress 
or  energy,  or  capacity  to  do  work  along  the  cord, 
which  we  can  measure  by  a  spring  balance 
inserted  in  place  of  the  cord  and  fixed  to  O,  and 
the  measure  of  that  stress  as  shown  by  the 

balance  is  m\  v\  and  in  different  circles  is  -  — • 

But  the  actual  stress  due  to  m\  =  ~  — ,  that  is 

2i 

easily  proven  by  using  another  mass  #z2  =  to  mi 
caused  to  revolve  by  an  extension  of  the  cord, 
forming  a  diameter  to  the  circle.  There  will 
then  be  a  balanced  stress  on  the  fixture,  and  the 


44  THEORY   OF   GRAVITATION. 

stress  on  the  extended  cord  will  be  m  v*,. 
although  two  equal  masses  m\  and  m<y  are  mov- 
ing in  the  circumference  with  equal  velocities, 

and  with  a  kinetic  energy  in  each  equal  to  —  —  * 

2i 

yet  the  stress  on  the  cord  does  not  alter  from 
m  v\  although  the  masses  and  the  kinetic 
energies  have  been  doubled,  which  proves  that  the 
transverse  stress  due  to  the  kinetic  energy  of  m 

2          m\i? 
is  not  m\  v  ,  but  —  —  -' 


Now  the  mass  m\  in  describing  the  complete 
circle  impinges  on  m,  and  gives  up  all  its  energy 
to  it,  that  is,  supposing  the  bodies  are  perfectly 
elastic  and  under  frictionless  conditions.  Now  m 
continues  with  its  original  velocity  in  A  B,  but 
where  is  the  transverse  stress  which  was  shown 
on  the  cord  whilst  describing  the  circle?  We 
know  it  is  not  in  m\  ,  which  is  perfectly  dead,  and 
as  no  energy  can  ever  be  destroyed  completely,  it 
must  be  in  some  way  attendant  to  m  in  its 
motion,  and  we  can  prove  that  it  accompanies  m 
as  a  latent  energy  capable  of  being  made  poten- 
tial by  means  of  a  radical  force,  and  such  quality 
of  motion  we  call  the  body's  kinetic  stability, 
and  we  have  shown  that  it  is  equal  to  the 

,  .      ..  m  v2 

kinetic  energy  =    —  —  ' 


THEORY    OF   GRAVITATION.  45 

PROPOSITION    IV. 

If  a  body  in  motion  in  a  straight  line  be  dis- 
turbed by  a  force  transverse  to  the  line  of  its 
motion,  and  the  amount  of  that  force  measured 
by  the  energy  it  produces  is  less  than  the  kinetic 
stability  of  the  body,  then  the  body  will  be  acted 
•on  by  a  force  tending  to  make  it  return  to  its 
original  line  of  motion,  and  such  a  force  I  call 
the  force  of  restitution,  and  its  value  is  equal  to 
the  difference  between  the  kinetic  stability  and 
the  amount  of  the  disturbing  force,  that  is, 

/r  =/g  =  £s  — /d  =  E*  — /d  =  £P  • 

On  the  proof  of  this  proposition  rests  the  most 
wonderful  property  of  energy,  the  elasticity  of 
motion,  the  golden  dream  of  all  philosophy. 
The  corner-stone  of  the  most  enduring  edifice 
which  science  can  ever  build,  whose  foundations 
were  laid  in  the  beginning  of  time,  and  on  whose 
glorious  turrets  rests  the  spiritual  emancipation 
of  the  human  soul. 

In  my  next  paper  I  will  prove  the  above  pro- 
position, and  show  its  application  to  mechanical 
invention.  We  will  now  conclude  by  stating  the 
Law  of  Kinetic  Stability. 

A  body  moving  in  free  space  with  independent 
motion  has  kinetic  energy  in  the  line  of  its  motion, 
and  kinetic  stability  tending  to  prevent  displace- 
ment transverse  to  its  line  of  motion  equal  to  its 


46  THEORY    OF    GRAVITATION. 

kinetic  energy,  and  should  a  radical  transverse- 
force  be  applied  equal  to  the  kinetic  stability,  the 
body  will  then  move  in  a  curvilinear  orbit  with  a 
velocity  equal  to  j/~2  X  v,  v  being  its  original' 
velocity,  and  according  as  the  transverse  radical 
force  is  greater  or  less  than  the  kinetic  stability,  so 
the  curve  will  be  one  of  less  or  greater  stability,  and 
the  force  of  restitution  will  be  less  or  greater. 

And  the  Law  of  the  Persistence  of  Energy: 

Every  body  moving  with  independent  free  motion 
in  a  straight  line  has  a  specific  tendency  to  continue 
in  that  line,  varying  with  and  always  equal  to  its 
kinetic  energy,  and  if  displaced  in  free  space  by  a 
transverse  force  there  will  always  be  an  unbalanced 
component  force  in  the  body' s  motion  tending  to 
bring  the  body  back  to  the  continued  line  of  its 
previous  motion. 

The  unbalanced  component  is  what  Newton 
ascribed  to  the  mutual  attraction  of  matter,  but 
which  we  now  know  is  due  to  the  Persistence  of 
Energy,  and  we  call  it  the  Force  of  Restitution. 
That  is  the  universal  force  of  gravitation;  it  is 
always  inversely  proportional  to  the  potential 
energy. 

Now  as  the  potential  energy  of  a  displaced 
force  varies  with  the  square  of  the  displacement, 
therefore  the  Force  of  Restitution,  due  to  the 
persistence  of  energy,  will  vary  inversely  as  the 


THEORY   OF  GRAVITATION.  47 

square  of  the  distance  or  displacement.  That  is 
the  geometrical  law,  and  is  true  for  kinematical 
motion,  but  the  great  kinetic  law  depends  on 
kinetic  and  centrifugal  energies. 


THE  KINETIC  THEORY  OF    GRAVITATION. 


PART  II. 

In  my  former  paper  on  '  'A  New  Theory  of  the 
Cause  of  the  Centripetal  Force,"  which  Newton 
and  his  followers  have  ascribed  to  the  mutual 
attraction  of  masses,  I  mentioned  the  fact  that  the 
kinetic  stability  of  a  body  which  has  independent 
motion  in  a  plane  normal  to  the  centripetal  force 
of  gravity,  would  tend  to  neutralize  the  apparent 
effect  of  that  force,  and  that  in  a  succeeding 
paper  I  would  show  how  that  result  was  pro- 
duced. 

In  the  discussion  on  the  paper  it  was  suggested 
by  some  members  that  the  question  was  of  suffi- 
cient importance  to  be  submitted  to  the  profes- 
sional scientists  at  Berkeley,  and  Palo  Alto. 

Professor  Soule  of  Berkeley  endorsed  my 
statement  that  the  experiment  of  the  catapult 


48  THEORY    OF    GRAVITATION. 

properly  carried  out  would  be  a  crucial  test. 
But  he  said  in  effect,  that  the  force  of  the  mutual 
attraction  of  masses  had  been  a  settled  doctrine 
in  science  so  long,  and  seemed  to  satisfy  every 
requirement,  that  he  would  not  be  prepared  to 
doubt  its  existence,  until  after  a  most  exhaustive 
proof  that  it  was  due  to  something  else. 

Exception  wras  also  taken  by  some  to  the  loose 
way  in  which  I  had  put  the  argument,  and  to 
the  want  of  details  in  the  catapult  experiment. 

The  experiment  was  one  of  many  which  I 
made  fifteen  years  ago,  when  I  first  doubted  the 
theory  of  attraction,  but  as  these  experiments 
were  not  carried  out  in  a  vacuum  I  did  not 
consider  them  sufficiently  exact  to  be  called 
scientific  experiments,  but  only  approximations, 
and  although  they  were  sufficiently  approximate 
to  show  me  that  a  body  in  motion  in  a  plane  at 
right  angles  to  the  force  of  gravity  did  not  fall 
with  the  same  centripetal  acceleration  that  the 
same  body  would  do  if  at  rest,  yet  they  were  not 
crucial  enough  to  place  before  the  Royal  Society 
of  lyondon. 

In  reading  up  the  subject  in  tracts,  published 
by  the  late  Dr.  Hutton  of  Woolwich  Academy, 
England,  on  the  experiments  in  gunnery,  I  found 
that  that  eminent  mathematician  had  noticed 
the  same  discrepancy  between  the  fall  of  bodies 


THEORY   OF   GRAVITATION.  49 

due  to  attraction,  and  the  practice  with  projectiles 
at  high  velocities,  which  he  ascribed  to  some 
polarized  condition  of  the  air.  (The  word  pol- 
arized, at  that  time  was  a  fashionable  fad  with 
scientists  for  explaining  away  any  discrepancy 
to  an  established  theory,  having  been  brought 
into  prominence  by  the  researches  of  Dr.  Thomas 
Young  and  Dr.  Brewster  in  connection  with  light. ) 

Nearly  every  scientist  since,  who  has  noted 
the  discrepancy,  has  tried  to  explain  it,  by 
supposing  the  projectile  to  kind  of  hypnotize  the 
layers  of  air  immediately  above  and  below  it,  so 
as  to  prevent  it  from  following  the  law  of  falling 
bodies  whilst  in  motion. 

Instead  of  accepting  that  explanation,  I  always 
felt  sure  there  was  some  other  cause  at  work, 
and  the  result  of  my  studies  and  experiments 
have  led  to  the  discovery  of  the  true  cause,  viz: 
that  the  persistence  of  energy,  and  the  accompany- 
ing kinetic  stability,  when  subjected  to  lateral 
forces,  is  the  true  cause  of  gravity. 

When  I  mentioned  the  matter  to  my  old 
professor,  Lord  Kelvin,  he  thought  kinetic  sta- 
bility was  too  intricate  a  mathematical  function, 
to  use  in  explaining  such  a  simple  matter,  and 
to  approach  the  subject  mathematically  from  that 
hypothesis  would  exhaust  the  methods  of  the 
analytical  calculus. 


50  THEORY   OF    GRAVITATION. 

Consequently  in  these  papers  I  prefer  to  go 
back  to  first  principles,  which  even  the  under- 
graduate can  understand  and  follow,  and  so  build 
up  my  theory  on  the  very  simplest  application  of 
the  laws  of  motion. 

In  the  discussion,  I  was  pleased  to  know  that 
Mr.  Richards,  a  past  president  of  the  Society 
had  given  the  weight  of  his  large  experience  in 
favor  of  the  theory  of  kinetic  stability  as  a 
probable  cause  of  centripetal  force,  in  preference 
to  Newton's  theory  of  attraction. 

He  finds  in  his  practice  many  actions  and 
reactions  in  high  speed  centrifugal  water  pumps, 
for  which  empirical  formulae  have  to  be  substi- 
tuted for  theory,  for  the  simple  reason  that  the 
present  theory  of  deviating  forces  does  not  meet 
the  requirements  of  the  case. 

Now  as  it  seems  to  be  the  almost  general  wish 
of  those  members  who  have  considered  the 
matter,  to  have  my  theory  submitted  to  one  or 
both  of  the  principal  universities  in  this  State,  I 
will  therefore  devote  this  paper  to  a  description 
of  the  experiments,  which,  if  carried  out  with 
scientific  accuracy,  will  prove  that  my  theory  is 
the  true  one. 

I  need  riot  call  attention  to  the  important 
results  to  science,  which  would  follow  from  the 
acceptance  of  the  theory  of  kinetic  stability  as  the 


THEORY   OF   GRAVITATION.  51 

true  proximate  cause  of  the  centripetal  force  of 
attraction  throughout  the  universe. 

The  past,  present  and  future  conditions  of  each 
planet,  not  only  physically,  but  vitally,  together 
with  all  the  actions  and  reactions  between  them 
and  their  primary,  would  be  calculable  from 
their  motions  alone. 

Whether  they  were  hollow  or  solid  spheroids; 
the  specific  heat  of  the  mass  of  each;  the 
extent  and  density  of  their  atmospheres;  the 
specific  force  of  gravity  on  their  surface;  the 
character  and  bodily  structure  of  their  inhabi- 
tants; would  all  become  mathematical  problems, 
depending  for  their  solution  on  the  ratio  of  the 
centripetal  to  the  centrifugal  energies  of  each 
planet. 

Then  when  we  carry  the  question  of  kinetic 
stability  into  molecular  physics,  it  opens  up  to 
exact  science  problems  which,  when  solved,  will 
revolutionize  all  our  ideas  of  matter,  soul  and 
spirit,  and  show  us  how  to  produce  and  control 
the  vast  latent  forces  of  nature,  with  greater 
efficiency  than  we  have  hitherto  dreamt  of. 

If  these  are  not  a  sufficient  encitement  to  a 
proper  determination  of  this  scientific  subject, 
then  the  love  of  truth  itself,  which  is  strong  in 
every  true  scientist,  should  be  motive  sufficient 
for  the  purpose. 


52  THEORY    OF    GRAVITATION. 

L,et  us  now  consider  proposition  IV. 

If  a  body  in  motion  in  a  straight  line,  having 

kinetic  energy  =    -— '  be    disturbed    by    a  force 

acting  transversely  to  the  line  of  its  motion;  if 
the  disturbing  force  be  any  finite  force  whatever, 
the  disturbed  body  will  describe  a  curve  as  the 
resultant  motion,  being  acted  on  by  two  effective 
components,  the  one  towards  the  instantaneous 
centre  of  curvature,  we  call  \\ieforce  of  restitution 
or  centripetal  force;  the  other  acting  normally  to 
the  centripetal  force,  we  call  the  tangential  f 01  ce. 

This  proposition  has  never  been  accepted 
hitherto  by  dynamical  science,  nor  to  my  know- 
ledge has  it  ever  been  completely  demonstrated. 

If  the  simple  action  of  two  impressed  forces 
acting  at  right  angles,  will  cause  a  body  to 
describe  a  curve  as  the  resultant  motion,  then 
where  is  the  need  for  the  mutual  attraction  of 
masses  to  cause  curvature? 

I  need  not  refer  to  the  established  principle  in 
dynamical  science,  called  the  resolution  of  forces 
or  motions,  which  proves  that  the  resultant  of 
two  forces  or  motions,  is  the  diagonal  of  the 
parallelogram  whose  adjacent  sides  represent  the 
forces  or  motions  in  amount  and  direction. 

That  I  acknowledge  as  a  cardinal  principle  of 
the  science  of  dynamics,  but  it  only  applies  to 


THEORY   OF   GRAVITATION.  53 

cases  of  constrained  motion,  and  I  am  dealing 
with  independent  motion  in  free  space. 

To  illustrate  my  meaning;  suppose  a  ball  be 
rolled  across  the  platform  of  a  car  in  motion, 
then  the  resultant  motion,  both  in  direction  and 
amount,  would  be  expressed  by  the  length  and 
direction  of  the  diagonal  of  the  parallelogram, 
whose  adjacent  sides  represented  the  direction 
and  amount  of  the  respective  motions. 

But  suppose  we  give  the  ball  a  certain  finite 
velocity  along  the  car,  independent  of  the  car's 
motion,  and  also  give  it  a  transverse  velocity 
across  the  car,  then  although  the  diagonal  of  the 
parallelogram  as  above  would  give  the  velocity 
due  to  the  constrained  motion  or  momentum,  yet 
the  resultant  of  the  independent  motion  would  be 
a  curve. 

I  can  demonstrate  that  fact  with  mathematical 
accuracy,  and  can  show  the  value  of  the  coordi- 
nates of  the  curve  under  various  forces,  and  one 
remarkable  result  of  the  geometry  of  the  subject 
is,  that  however  small  the  kinetic  energy  of  the 
body  may  be,  so  long  as  it  is  Jinite;  and  however 
great  the  transverse  deviating  force  may  be,  if  it 
is  not  infinite,  the  body  can  never  be  permanently 
displaced  from  the  original  line  of  motion,  but 
will  always  have  a  component  force  acting  as 
Newton's  centripetal  force  apparently  towards  a 
focus. 


54  THEORY   OP   GRAVITATION. 

And  that  is  a  most  wonderful  fact  which 
explains  the  constitution  of  the  universe  as  a 
stable  or  conservative  system,  which  no  radical 
force  less  than  that  of  Omnipotence  can  ever 
destroy. 

And  it  also  teaches  us  another  most  wonderful 
principle  in  the  constitution  of  the  universe,  viz: 
that  the  forces  necessary  to  give  it  stability,  must 
have  been  controlled  and  directed  by  some  power 
independent  of  and  unaffected  by  the  phenomena 
produced. 

That  in  fact  the  Creator  of  the  physical 
universe,  must  have  done  work  to  produce  the 
phenomena  which  we  call  the  universe.  It  is 
that  principle  of  independent  action,  which  act- 
ing against  kinetic  stability  makes  stable  motion. 

Again  let  me  explain  my  meaning.  If  a  body 
like  a  railway  train,  or  a  cannon  ball,  be  con- 
strained to  move  in  a  curve,  by  means  of  a  fric- 
tionless  guide,  then  no  additional  energy  has  been 
communicated  from  without,  but  simply  the 
resistance  of  a  frictionless  guide;  hence  no  energy 
has  been  added  or  extracted  from  the  moving 
body.  The  orbit  has  been  described  by  means 
of  the  inherent  energy,  or  vis  viva  of  the  body, 
and  the  result  is  that  the  moment  the  guide  is 
removed,  be  it  a  string  fixed  at  a  centre,  or  an 
attractive  force  from  a  centre,  or  a  rigid  friction- 


THEORY  OF   GRAVITATION.  55 

less  guide,  then  the  moment  that  it  is  removed 
the  body  goes  off  on  a  tangent  to  the  curve  it  has 
been  constrained  to  move  in. 

But  suppose  the  cannon  ball  receive  an  impulse 
from  an  independent  outside  force,  acting  trans- 
versely to  the  line  of  motion  of  the  cannon  ball, 
equal  to  twice  the  kinetic  energy  of  the  ball, 
then  the  ball  will  forever  move  in  an  orbit  which 
is  curvilinear,  and  if  the  deviating  force  exceed 
twice  the  kinetic  energy,  the  ball  will  move  in 
an  orbit  which  is  an  ellipse  of  any  eccentricity 
whose  centripetal  force  will  vary  inversely  as  the 
square  of  the  distance  from  one  of  the  foci,  and 
the  resultant  motion  is  perfectly  stable,  the  same 
as  the  universe,  or  the  solar  system. 

As  the  mathematical  proof  of  this  proposition 
is  purely  theoretical,  I  will  not  complicate  this 
paper  by  introducing  it  here,  but  will  proceed  to 
sketch  out  a  method  of  experimental  demon- 
stration, which  will  establish  the  fact  that  curvi- 
linear motion  is  the  true  resultant  in  all  free 
independent  motions. 

EXPERIMENT   I. 

Take  a  slab  of  polished  marble  or  glass,  or  any 
other  polished  surface,  perfectly  horizontal,  or 
level  in  every  direction  on  the  surface,  about 
fifty  feet  long,  and  ten  feet  broad.  At  one  end 
fix  a  catapult  arrangement,  which  will  project 


UHI7BRSIT7 


56  THEORY   OF   GRAVITATION. 

a  spherical  steel  ball  (of  the  size  of  a  billiard 
ball),  along  the  top  of  this  slab  in  a  straight  line 
longitudinally  with  a  velocity  of  one  hundred 
feet  per  second. 

About  one  foot  from  the  initial  point  of  motion 
of  the  longitudinal  catapult,  place  a  transverse 
catapult,  having  its  initial  point  of  motion  one 
foot  from  the  line  of  the  other.  Let  both  cata- 
pults be  capable  of  giving  the  same  velocity  to 
the  same  §ized  balls  of  steel.  Let  the  springs  of 
both  catapults  be  held  back  by  the  one  string, 
the  centre  of  which  is  placed  between  the  carbon 
points  of  an  electric  machine,  which  by  burning 
the  string  allowed  both  catapults  to  act  instanta- 
neously. Then,  if  proper  precautions  are  taken, 
the  transverse  ball  will  strike  the  longitudinal 
ball  one  foot  from  its  initial  point,  with  the  same 
kinetic  energy  as  the  longitudinal  ball  has. 

The  resultant  motion  of  the  longitudinal  ball 
will  be  curvilinear,  and  whatever  energy  the 
transverse  ball  loses,  the  other  will  receive,  less 
the  friction  of  course  and  the  viscosity  of  the 
balls,  and  the  various  energies  of  heat,  light  and 
electricity,  dissipated  by  the  concussion.  The 
curve  can  be  shown  by  having  a  black  slab  and 
a  whitened  ball. 

By  careful  experiment  in  a  vacuum,  with 
various  degrees  of  energy,  the  coordinates  of 
various  curves  can  by  this  means  be  almost 
exactly  determined,  and  so  one  of  the  most 
important  principles  in  the  whole  realm  of  dyna- 
mical science  can  be  demonstrated  by  experi- 
ment. And  I  have  no  hesitation  in  saying,  that 
the  professor,  and  the  university,  which  demon- 
strates the  truth  of  this  principle  most  correctly, 
will  earn  for  themselves  a  name  and  a  fame, 
which  will  be  esteemed  and  honored  whilst  the 
world  lasts. 


THEORY   OF   GRAVITATION.  57 

To  such  an  institution  the  ambitious  youths 
from  every  nation  will  come  for  instruction, 
because  the  establishment  of  this  principle  of 
kinetic  stability,  is  one  of  more  far  reaching 
importance  to  science  in  general,  than  we  can 
imagine  at  present,  as  not  only  physical  phe- 
nomena, but  vital  and  spiritual  phenomena  all 
depend  on  it  largely  for  true  scientific  treatment. 
In  this  great  principle  resides  the  hidden  power 
which  through  the  method  of  evolution  does  its 
work.  And  on  this  latent  energy  depends  the 
influence  which  enables  faith  to  control  the 
phenomena  of  the  spiritual  world. 

The  theoretical  proof  will  be  given  by  me  in 
another  paper,  as  soon  as  the  experimental  proof 
is  ready  for  publication;  to  show  what  is  the 
difference  between  theory  and  experiment.  A 
knowledge  of  the  theory  tends  to  make  the 
experimenter  imaginative,  and  unreliable  in  the 
statement  of  results,  hence  the  theoretical  demon- 
stration will  be  witheld  for  the  present. 

The  second  problem  is  to  prove  experimentally, 
that  a  body  near  the  surface  of  the  earth  moving 
horizontally  with  kinetic  energy,  will  not  be 
influenced  by  the  force  of  gravity  with  the  same 
acceleration  towards  the  centre  of  the  earth,  as 
if  the  same  body  had  been  at  rest  relative  to  the 
earth.  Or  in  other  words,  a  horizontal  projectile 


58  THEORY   OF   GRAVITATION. 

moving  one  hundred  feet  in  one  second,  will  not 
fall  sixteen  feet  during  that  second. 

To  prove  this  by  experiment  exactly,  and  find 
the  law  of  its  acceleration  under  various  horizon- 
tal velocities,  requires  a  very  complete  and 
elaborate  apparatus,  such  as  only  a  university 
can  provide,  but  this  would  be  a  crucial  test  of 
the  two  theories: 

Kinetic  stability  versus  attraction  of  matter,  and 
as  I  know  that  kinetic  stability  is  the  true  one, 
and  is  bound  in  the  near  future  to  work  a  great 
revolution  in  all  science,  it  is  well  worthy  the 
earnest  attention  of  all  teachers  of  science,  and 
those  who  wished  to  be  honored  as  the  leaders  of 
the  scientific  world,  will  do  well  to  look  to  their 
laurels. 

Here  is  a  simple  experiment,  .which  if  carried 
out  carefully  in  a  vacuum  will  upset  the  best- 
established  theory  in  all  the  domain  of  natural 
science,  which  will  cause  half  of  the  scientific 
books  in  the  world  to  be  re- written. 

Can  we  rest  satisfied,  and  continue  to  teach  fal- 
lacies to  the  world,  and  dignify  them  with  the 
name  of  science,  when  such  a  simple  experiment 
will  forever  correct  and  remove  this  error? 

Although  this  proposition  can  also  be  demon- 
strated with  mathematical  accuracy  by  using  the 
principle  of  kinetic  stability,  yet  the  three  laws 


THEORY   OF   GRAVITATION.  59 

of  motion  will  not  enable  us  to  demonstrate  it, 
hence  it  is  necessary  that  an  experiment  of  a 
crucial  character  should  establish  the  fact  before 
the  scientific  world  will  believe  in  it. 

Now  the  question  is,  to  which  university  shall 
the  honor  belong  in  having  with  the  strictest 
scientific  accuracy  demonstrated  to  the  world  this 
important  fact;  viz:  that  a  body  moving  horizon- 
tally with  independent  motion  will  not  fall  six- 
teen feet  in  one  second,  the  distance  it  would  fall 
if  at  rest? 

Although  I  would  prefer  to  leave  to  the  experi- 
menter the  choice  of  methods  to  determine  the 
truth,  yet  there  are  certain  precautions  to  be 
taken  which  it  may  be  well  for  me  to  mention. 

1st.  The  experiment  must  be  carried  out  in  a 
vacuum,  as  explanations  have  already  been 
attempted,  to  prove  that  the  air  carries  the  body, 
and  vSO  prevents  the  fall. 

2nd.  The  velocity  should  exceed  fifty  feet  per 
second. 

3rd.  The  apparatus  should  be  as  rigid  and 
unaffected  by  vibration  as  possible. 

4th.  The  air-exhausted  tube  or  case  should  be 
at  least  fifty  feet  long  with  a  properly -stretched 
diaphragm  mounted  on  a  square  frame  placed  at 
distances  apart  of  one  foot;  two  transverse  lines 
cutting  each  other  at  the  center  of  the  dia- 


60  THEORY    OF    GRAVITATION. 

phragm,  as  impressions  or  water  marks  in  the 
diaphragms  should  be  ranged  exactly  by  means 
ot  a  transit  instrument,  the  diaphragms  should 
be  white  and  the  projectile  blackened. 

5th.  The  vacuous  box  should  have  one  side 
removable  with  great  ease  to  enable  the  trajec- 
tory to  be  exactly  measured. 

6th.  The  time  should  be  if  possible  one 
second. 

As  the  value  of  this  experiment  to  mechanical 
and  astronomical  science  cannot  be  overestimated, 
it  behooves  the  experimenter  to  use  the  greatest 
care  in  devising  and  describing  each  and  every 
detail. 

As  aerial  locomotion  is  bound  to  depend  very 
largely  on  the  fact  that  a  body  in  motion  does 
not  fall  the  prescribed  sixteen  feet  in  a  second,  it 
can  easily  be  seen  of  what  immense  importance 
the  knowledge  of  this  fact  will  be  to  the  mechani- 
cal and  political  world. 

Important  as  that  fact  is  to  mechanics,  it  is  no 
less  so  to  astronomy,  as  the  law  of  attraction 
depends  at  present  on  the  multiplication  of 
masses.  If  10  units  of  mass  be  multiplied  by  20 
units  of  mass  the  resultant  attraction  is  at 
present  equal  to  200  units  of  mass,  but  we  know 
that  the  quantity  of  matter  contained  in  two 
bodies,  one  of  which  contains  10  unks  of  matter, 


THEORY   OF   GRAVITATION.  61 

and  the  other  20  units  of  matter,  can  never  be 
more  than  30  units  of  matter. 

Now  although  the  law  of  the  inverse  square  of 
the  distance  enables  astronomers  to  make  close 
approximation  in  the  motions  of  the  planets,  the 
law  of  the  multiplication  of  the  masses  enables 
them  to  make  ignorant  guesses  at  the  specific 
gravity  of  each  planet,  and  the  specific  heat 
which  the  mass  contains,  and  by  this  means  the 
world  is  kept  in  complete  ignorance  of  the  con- 
ditions of  the  inhabitants  in  the  other  planets. 

Now  when  we  look  at  this  subject  from  every 
possible  point,  it  behooves  us  as  a  Society,  either 
to  act  alone,  or  in  conjunction  with  the  Astronom- 
ical Society,  and  use  all  the  influence  possible  to 
have  this  matter  correctly  determined  by  one  or 
both  of  our  great  universities. 

It  behooves  us  also  to  act  promptly,  as  the 
matter  will  be  taken  up  by  other  institutions  in 
the  Eastern  States,  who,  from  the  many  let- 
ters I  receive,  seem  to  be  acting  in  earnest,  and 
appear  to  take  more  interest  in  the  subject  than 
the  scientists  of  this  Coast. 

That  California  should  have  the  high  honor  of 
demonstrating  to  the  world  the  principles  of 
kinetic  stability,  and  proving  that  the  force  of 
the  mutual  attraction  of  masses  is  simply  a  fal- 
lacy and  a  delusion,  is  the  most  sincere  wish  of 
a  humble  member  of  the  Technical  Society. 

gsSS. 

or  THB 

'innVBKSITT 


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